Routine PSGEHRD() Documented By Universal Report

Routine: PSGEHRD()

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# Variables:	63
# Callers:	0
# Callings:	3
# Words:	153
# Keywords:	86

..
     .. Array Arguments ..
     ..
  Purpose
  =======
  PSGEHRD reduces a real general distributed matrix sub( A )
  to upper Hessenberg form H by an orthogonal similarity transforma-
  tion:  Q' * sub( A ) * Q = H, where
  sub( A ) = A(IA+N-1:IA+N-1,JA+N-1:JA+N-1).
  Notes
  =====
  Each global data object is described by an associated description
  vector.  This vector stores the information required to establish
  the mapping between an object element and its corresponding process
  and memory location.
  Let A be a generic term for any 2D block cyclicly distributed array.
  Such a global array has an associated description vector DESCA.
  In the following comments, the character _ should be read as
  "of the global array".
  NOTATION        STORED IN      EXPLANATION
  --------------- -------------- --------------------------------------
  DTYPE_A(global) DESCA( DTYPE_ )The descriptor type.  In this case,
                                 DTYPE_A = 1.
  CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
                                 the BLACS process grid A is distribu-
                                 ted over. The context itself is glo-
                                 bal, but the handle (the integer
                                 value) may vary.
  M_A    (global) DESCA( M_ )    The number of rows in the global
                                 array A.
  N_A    (global) DESCA( N_ )    The number of columns in the global
                                 array A.
  MB_A   (global) DESCA( MB_ )   The blocking factor used to distribute
                                 the rows of the array.
  NB_A   (global) DESCA( NB_ )   The blocking factor used to distribute
                                 the columns of the array.
  RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
                                 row of the array A is distributed.
  CSRC_A (global) DESCA( CSRC_ ) The process column over which the
                                 first column of the array A is
                                 distributed.
  LLD_A  (local)  DESCA( LLD_ )  The leading dimension of the local
                                 array.  LLD_A >= MAX(1,LOCr(M_A)).
  Let K be the number of rows or columns of a distributed matrix,
  and assume that its process grid has dimension p x q.
  LOCr( K ) denotes the number of elements of K that a process
  would receive if K were distributed over the p processes of its
  process column.
  Similarly, LOCc( K ) denotes the number of elements of K that a
  process would receive if K were distributed over the q processes of
  its process row.
  The values of LOCr() and LOCc() may be determined via a call to the
  ScaLAPACK tool function, NUMROC:
          LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
          LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
  An upper bound for these quantities may be computed by:
          LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
          LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
  Arguments
  =========
  N       (global input) INTEGER
          The number of rows and columns to be operated on, i.e. the
          order of the distributed submatrix sub( A ). N >= 0.
  ILO     (global input) INTEGER
  IHI     (global input) INTEGER
          It is assumed that sub( A ) is already upper triangular in
          rows IA:IA+ILO-2 and IA+IHI:IA+N-1 and columns JA:JA+ILO-2
          and JA+IHI:JA+N-1. See Further Details. If N > 0,
          1 <= ILO <= IHI <= N; otherwise set ILO = 1, IHI = N.
  A       (local input/local output) REAL pointer into the
          local memory to an array of dimension (LLD_A,LOCc(JA+N-1)).
          On entry, this array contains the local pieces of the N-by-N
          general distributed matrix sub( A ) to be reduced. On exit,
          the upper triangle and the first subdiagonal of sub( A ) are
          overwritten with the upper Hessenberg matrix H, and the ele-
          ments below the first subdiagonal, with the array TAU, repre-
          sent the orthogonal matrix Q as a product of elementary
          reflectors. See Further Details.
  IA      (global input) INTEGER
          The row index in the global array A indicating the first
          row of sub( A ).
  JA      (global input) INTEGER
          The column index in the global array A indicating the
          first column of sub( A ).
  DESCA   (global and local input) INTEGER array of dimension DLEN_.
          The array descriptor for the distributed matrix A.
  TAU     (local output) REAL array, dimension LOCc(JA+N-2)
          The scalar factors of the elementary reflectors (see Further
          Details). Elements JA:JA+ILO-2 and JA+IHI:JA+N-2 of TAU are
          set to zero. TAU is tied to the distributed matrix A.
  WORK    (local workspace/local output) REAL array,
                                                    dimension (LWORK)
          On exit, WORK( 1 ) returns the minimal and optimal LWORK.
  LWORK   (local or global input) INTEGER
          The dimension of the array WORK.
          LWORK is local input and must be at least
          LWORK >= NB*NB + NB*MAX( IHIP+1, IHLP+INLQ )
          where NB = MB_A = NB_A, IROFFA = MOD( IA-1, NB ),
          ICOFFA = MOD( JA-1, NB ), IOFF = MOD( IA+ILO-2, NB ),
          IAROW = INDXG2P( IA, NB, MYROW, RSRC_A, NPROW ),
          IHIP = NUMROC( IHI+IROFFA, NB, MYROW, IAROW, NPROW ),
          ILROW = INDXG2P( IA+ILO-1, NB, MYROW, RSRC_A, NPROW ),
          IHLP = NUMROC( IHI-ILO+IOFF+1, NB, MYROW, ILROW, NPROW ),
          ILCOL = INDXG2P( JA+ILO-1, NB, MYCOL, CSRC_A, NPCOL ),
          INLQ = NUMROC( N-ILO+IOFF+1, NB, MYCOL, ILCOL, NPCOL ),
          INDXG2P and NUMROC are ScaLAPACK tool functions;
          MYROW, MYCOL, NPROW and NPCOL can be determined by calling
          the subroutine BLACS_GRIDINFO.
          If LWORK = -1, then LWORK is global input and a workspace
          query is assumed; the routine only calculates the minimum
          and optimal size for all work arrays. Each of these
          values is returned in the first entry of the corresponding
          work array, and no error message is issued by PXERBLA.
  INFO    (global output) INTEGER
          = 0:  successful exit
          < 0:  If the i-th argument is an array and the j-entry had
                an illegal value, then INFO = -(i*100+j), if the i-th
                argument is a scalar and had an illegal value, then
                INFO = -i.
  Further Details
  ===============
  The matrix Q is represented as a product of (ihi-ilo) elementary
  reflectors
     Q = H(ilo) H(ilo+1) . . . H(ihi-1).
  Each H(i) has the form
     H(i) = I - tau * v * v'
  where tau is a real scalar, and v is a real vector with
  v(1:I) = 0, v(I+1) = 1 and v(IHI+1:N) = 0; v(I+2:IHI) is stored on
  exit in A(IA+ILO+I:IA+IHI-1,JA+ILO+I-2), and tau in TAU(JA+ILO+I-2).
  The contents of A(IA:IA+N-1,JA:JA+N-1) are illustrated by the follow-
  ing example, with N = 7, ILO = 2 and IHI = 6:
  on entry                         on exit
  ( a   a   a   a   a   a   a )    (  a   a   h   h   h   h   a )
  (     a   a   a   a   a   a )    (      a   h   h   h   h   a )
  (     a   a   a   a   a   a )    (      h   h   h   h   h   h )
  (     a   a   a   a   a   a )    (      v2  h   h   h   h   h )
  (     a   a   a   a   a   a )    (      v2  v3  h   h   h   h )
  (     a   a   a   a   a   a )    (      v2  v3  v4  h   h   h )
  (                         a )    (                          a )
  where a denotes an element of the original matrix sub( A ), H denotes
  a modified element of the upper Hessenberg matrix H, and vi denotes
  an element of the vector defining H(JA+ILO+I-2).
  Alignment requirements
  ======================
  The distributed submatrix sub( A ) must verify some alignment proper-
  ties, namely the following expression should be true:
  ( MB_A.EQ.NB_A .AND. IROFFA.EQ.ICOFFA )
  =====================================================================
     .. Parameters ..

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001        SUBROUTINE PSGEHRD( N , ILO , IHI , A , IA , JA , DESCA , TAU , WORK ,
002       $LWORK , INFO )
003  
004  *     -- ScaLAPACK routine(version 1.7) --
005  *     University of Tennessee , Knoxville , Oak Ridge National Laboratory ,
006  *     and University of California , Berkeley.
007  *     May 25 , 2001
008  
009  *     .. Scalar Arguments ..
010        INTEGER IA , IHI , ILO , INFO , JA , LWORK , N
011        INTEGER BLOCK_CYCLIC_2D , CSRC_ , CTXT_ , DLEN_ , DTYPE_ ,
012       $LLD_ , MB_ , M_ , NB_ , N_ , RSRC_
013        PARAMETER( BLOCK_CYCLIC_2D = 1 , DLEN_ = 9 , DTYPE_ = 1 ,
014       $CTXT_ = 2 , M_ = 3 , N_ = 4 , MB_ = 5 , NB_ = 6 ,
015       $RSRC_ = 7 , CSRC_ = 8 , LLD_ = 9 )
016        REAL ONE , ZERO
017        PARAMETER( ONE = 1.0E + 0 , ZERO = 0.0E + 0 )
018  *     ..
019  *     .. Local Scalars ..
020        LOGICAL LQUERY
021        CHARACTER COLCTOP , ROWCTOP
022        INTEGER I , IACOL , IAROW , IB , ICOFFA , ICTXT , IHIP ,
023       $IHLP , IIA , IINFO , ILCOL , ILROW , IMCOL , INLQ ,
024       $IOFF , IPT , IPW , IPY , IROFFA , J , JJ , JJA , JY ,
025       $K , L , LWMIN , MYCOL , MYROW , NB , NPCOL , NPROW ,
026       $NQ
027        REAL EI
028  *     ..
029  *     .. Local Arrays ..
030        INTEGER DESCY( DLEN_ ) , IDUM1( 3 ) , IDUM2( 3 )
031  *     ..
032  *     .. External Subroutines ..
033        EXTERNAL BLACS_GRIDINFO , CHK1MAT , DESCSET , INFOG1L ,
034       $INFOG2L , PCHK1MAT , PSGEMM , PSGEHD2 ,
035       $PSLAHRD , PSLARFB , PB_TOPGET , PB_TOPSET , PXERBLA
036  *     ..
037  *     .. External Functions ..
038        INTEGER INDXG2P , NUMROC
039        EXTERNAL INDXG2P , NUMROC
040  *     ..
041  *     .. Intrinsic Functions ..
042        INTRINSIC MAX , MIN , MOD , REAL
043  *     ..
044  *     .. Executable Statements ..
045  
046  *     Get grid parameters
047  
048        ICTXT = DESCA( CTXT_ )
049        CALL BLACS_GRIDINFO( ICTXT , NPROW , NPCOL , MYROW , MYCOL )
050  
051  *     Test the input parameters
052  
053        INFO = 0
054        IF( NPROW.EQ. - 1 ) THEN
054               
055            INFO = - (700 + CTXT_)
056        ELSE
056               
057            CALL CHK1MAT( N , 1 , N , 1 , IA , JA , DESCA , 7 , INFO )
058            IF( INFO.EQ.0 ) THEN
058                   
059                NB = DESCA( NB_ )
060                IROFFA = MOD( IA - 1 , NB )
061                ICOFFA = MOD( JA - 1 , NB )
062                CALL INFOG2L( IA , JA , DESCA , NPROW , NPCOL , MYROW , MYCOL ,
063       $        IIA , JJA , IAROW , IACOL )
064                IHIP = NUMROC( IHI + IROFFA , NB , MYROW , IAROW , NPROW )
065                IOFF = MOD( IA + ILO - 2 , NB )
066                ILROW = INDXG2P( IA + ILO - 1 , NB , MYROW , DESCA( RSRC_ ) ,
067       $        NPROW )
068                IHLP = NUMROC( IHI - ILO + IOFF + 1 , NB , MYROW , ILROW , NPROW )
069                ILCOL = INDXG2P( JA + ILO - 1 , NB , MYCOL , DESCA( CSRC_ ) ,
070       $        NPCOL )
071                INLQ = NUMROC( N - ILO + IOFF + 1 , NB , MYCOL , ILCOL , NPCOL )
072                LWMIN = NB*( NB + MAX( IHIP + 1 , IHLP + INLQ ) )
073  
074                WORK( 1 ) = REAL( LWMIN )
075                LQUERY =( LWORK.EQ. - 1 )
076                IF( ILO.LT.1 .OR. ILO.GT.MAX( 1 , N ) ) THEN
076                       
077                    INFO = - 2
078                ELSE IF( IHI.LT.MIN( ILO , N ) .OR. IHI.GT.N ) THEN
078                       
079                    INFO = - 3
080                ELSE IF( IROFFA.NE.ICOFFA .OR. IROFFA.NE.0 ) THEN
080                       
081                    INFO = - 6
082                ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN
082                       
083                    INFO = - (700 + NB_)
084                ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
084                       
085                    INFO = - 10
086                END IF
087            END IF
088            IDUM1( 1 ) = ILO
089            IDUM2( 1 ) = 2
090            IDUM1( 2 ) = IHI
091            IDUM2( 2 ) = 3
092            IF( LWORK.EQ. - 1 ) THEN
092                   
093                IDUM1( 3 ) = - 1
094            ELSE
094                   
095                IDUM1( 3 ) = 1
096            END IF
097            IDUM2( 3 ) = 10
098            CALL PCHK1MAT( N , 1 , N , 1 , IA , JA , DESCA , 7 , 3 , IDUM1 , IDUM2 ,
099       $    INFO )
100        END IF
101  
102        IF( INFO.NE.0 ) THEN
102               
103            CALL PXERBLA( ICTXT , 'PSGEHRD' , - INFO )
104            RETURN
105        ELSE IF( LQUERY ) THEN
105               
106            RETURN
107        END IF
108  
109  *     Set elements JA : JA + ILO - 2 and JA + JHI - 1 : JA + N - 2 of TAU to zero.
110  
111        NQ = NUMROC( JA + N - 2 , NB , MYCOL , DESCA( CSRC_ ) , NPCOL )
112        CALL INFOG1L( JA + ILO - 2 , NB , NPCOL , MYCOL , DESCA( CSRC_ ) , JJ ,
113       $IMCOL )
114        DO 10 J = JJA , MIN( JJ , NQ )
114               
115            TAU( J ) = ZERO
116     10 CONTINUE
117  
118        CALL INFOG1L( JA + IHI - 1 , NB , NPCOL , MYCOL , DESCA( CSRC_ ) , JJ ,
119       $IMCOL )
120        DO 20 J = JJ , NQ
120               
121            TAU( J ) = ZERO
122     20 CONTINUE
123  
124  *     Quick return if possible
125  
126        IF( IHI - ILO.LE.0 )
126               
127       $    RETURN
128  
129            CALL PB_TOPGET( ICTXT , 'Combine' , 'Columnwise' , COLCTOP )
130            CALL PB_TOPGET( ICTXT , 'Combine' , 'Rowwise' , ROWCTOP )
131            CALL PB_TOPSET( ICTXT , 'Combine' , 'Columnwise' , '1 - tree' )
132            CALL PB_TOPSET( ICTXT , 'Combine' , 'Rowwise' , '1 - tree' )
133  
134            IPT = 1
135            IPY = IPT + NB * NB
136            IPW = IPY + IHIP * NB
137            CALL DESCSET( DESCY , IHI + IROFFA , NB , NB , NB , IAROW , ILCOL , ICTXT ,
138       $    MAX( 1 , IHIP ) )
139  
140            K = ILO
141            IB = NB - IOFF
142            JY = IOFF + 1
143  
144  *         Loop over remaining block of columns
145  
146            DO 30 L = 1 , IHI - ILO + IOFF - NB , NB
146                   
147                I = IA + K - 1
148                J = JA + K - 1
149  
150  *             Reduce columns j : j + ib - 1 to Hessenberg form , returning the
151  *             matrices V and T of the block reflector H = I - V*T*V'
152  *             which performs the reduction , and also the matrix Y = A*V*T
153  
154                CALL PSLAHRD ( IHI , K , IB , A , IA , J , DESCA , TAU , WORK( IPT ) ,
155       $        WORK( IPY ) , 1 , JY , DESCY , WORK( IPW ) )
156  
157  *             Apply the block reflector H to A(ia : ia + ihi - 1 , j + ib : ja + ihi - 1)
158  *             from the right , computing A := A - Y * V'.
159  *             V(i + ib , ib - 1) must be set to 1.
160  
161                CALL PSELSET2( EI , A , I + IB , J + IB - 1 , DESCA , ONE )
162                CALL PSGEMM( 'No transpose' , 'Transpose' , IHI , IHI - K - IB + 1 , IB ,
163       $        - ONE , WORK( IPY ) , 1 , JY , DESCY , A , I + IB , J ,
164       $        DESCA , ONE , A , IA , J + IB , DESCA )
165                CALL PSELSET( A , I + IB , J + IB - 1 , DESCA , EI )
166  
167  *             Apply the block reflector H to A(i + 1 : ia + ihi - 1 , j + ib : ja + n - 1) from
168  *             the left
169  
170                CALL PSLARFB ( 'Left' , 'Transpose' , 'Forward' , 'Columnwise' ,
171       $        IHI - K , N - K - IB + 1 , IB , A , I + 1 , J , DESCA ,
172       $        WORK( IPT ) , A , I + 1 , J + IB , DESCA , WORK( IPY ) )
173  
174                K = K + IB
175                IB = NB
176                JY = 1
177                DESCY( CSRC_ ) = MOD( DESCY( CSRC_ ) + 1 , NPCOL )
178  
179     30     CONTINUE
180  
181  *         Use unblocked code to reduce the rest of the matrix
182  
182               
183            CALL PSGEHD2 ( N , K , IHI , A , IA , JA , DESCA , TAU , WORK , LWORK ,
184       $    IINFO )
185  
186            CALL PB_TOPSET( ICTXT , 'Combine' , 'Columnwise' , COLCTOP )
187            CALL PB_TOPSET( ICTXT , 'Combine' , 'Rowwise' , ROWCTOP )
188  
189            WORK( 1 ) = REAL( LWMIN )
190  
191            RETURN
192  
193  *         End of PSGEHRD
194  
195        END3233

Variables in Routine PSGEHRD()

Summary Report
Data Type	Quantity	Size(byte)
CHARACTER	2	2
INTEGER	55	240
LOGICAL	1	1
REAL	5	20
TOTAL	63	263

List of Variables

CHARACTER

COLCTOP ROWCTOP

INTEGER

BLOCK_CYCLIC_2D CSRC_ CTXT_ DESCY( DLEN_ ) DLEN_
DTYPE_ I IA IACOL IAROW
IB ICOFFA ICTXT IDUM1( 3 ) IDUM2( 3 )
IHI IHIP IHLP IIA IINFO
ILCOL ILO ILROW IMCOL INDXG2P
INFO INLQ IOFF IPT IPW
IPY IROFFA J JA JJ
JJA JY K L LLD_
LWMIN LWORK M_ MB_ MYCOL
MYROW N N_ NB NB_
NPCOL NPROW NQ NUMROC RSRC_

LOGICAL

LQUERY

REAL

EI ONE TAU WORK ZERO

Variables Dependence Graph
Put the mouse over a right hand side variable to display the corresponding line of the dependence
-
- -
DESCY <--- CSRC_, DESCY, NPCOL

I <--- IAI = IA + K - 1, KI = IA + K - 1

IB <--- IOFFIB = NB - IOFF, NBIB = NB - IOFF{2IB = NB}

ICOFFA <--- JAICOFFA = MOD( JA-1, NB ), NBICOFFA = MOD( JA-1, NB )

ICTXT <--- CTXT_ICTXT = DESCA( CTXT_ )

IDUM1 <--- IHIIDUM1( 2 ) = IHI, ILOIDUM1( 1 ) = ILO

IHIP <--- IAROW, IHI, IROFFA, MYROW, NB, NPROW, NUMROC

IHLP <--- IHI, ILO, ILROW, IOFF, MYROW, NB, NPROW, NUMROC

ILCOL <--- ILO, INDXG2P, CSRC_, JA, MYCOL, NB, NPCOL

ILROW <--- IA, ILO, INDXG2P, MYROW, NB, NPROW, RSRC_

INFO <--- CTXT_INFO = -(700+CTXT_), NB_INFO = -(700+NB_)

INLQ <--- ILCOL, ILO, IOFF, MYCOL, N, NB, NPCOL, NUMROC

IOFF <--- IAIOFF = MOD( IA+ILO-2, NB ), ILOIOFF = MOD( IA+ILO-2, NB ), NBIOFF = MOD( IA+ILO-2, NB )

IPW <--- IHIPIPW = IPY + IHIP * NB, IPYIPW = IPY + IHIP * NB, NBIPW = IPY + IHIP * NB

IPY <--- IPTIPY = IPT + NB * NB, NBIPY = IPT + NB * NB

IROFFA <--- IAIROFFA = MOD( IA-1, NB ), NBIROFFA = MOD( IA-1, NB )

J <--- JAJ = JA + K - 1, JJDO 10 J = JJA, MIN( JJ, NQ ){2DO 20 J = JJ, NQ}, JJADO 10 J = JJA, MIN( JJ, NQ ), KJ = JA + K - 1, NQDO 10 J = JJA, MIN( JJ, NQ ){2DO 20 J = JJ, NQ}

JY <--- IOFFJY = IOFF + 1

K <--- IBK = K + IB, ILOK = ILO, KK = K + IB

L <--- IHIDO 30 L = 1, IHI-ILO+IOFF-NB, NB, ILODO 30 L = 1, IHI-ILO+IOFF-NB, NB, IOFFDO 30 L = 1, IHI-ILO+IOFF-NB, NB, NBDO 30 L = 1, IHI-ILO+IOFF-NB, NB

LWMIN <--- IHIP, IHLP, INLQ, NB

NB <--- NB_NB = DESCA( NB_ )

NQ <--- CSRC_, JA, MYCOL, N, NB, NPCOL, NUMROC

TAU <--- ZEROTAU( J ) = ZERO{2TAU( J ) = ZERO}

WORK <--- LWMINWORK( 1 ) = REAL( LWMIN ){2WORK( 1 ) = REAL( LWMIN )}

Analysis elements of the routine PSGEHRD()
Put the mouse over each element to display detailed matching information

Assigned variables
		A , BLOCK_CYCLIC_2D , CSRC_ , CTXT_ , DLEN_ , DTYPE_ , I , IB , ICOFFA , ICTXT , IDUM1 , IDUM2 , IHIP , IHLP , ILCOL , ILROW , INFO , INLQ , IOFF , IPT , IPW , IPY , IROFFA , J , JY , K , L , LLD_ , LQUERY , LWMIN , M_ , MB_ , N_ , NB , NB_ , NQ , ONE , RSRC_ , WORK , ZERO

Active variables
		A , BLOCK_CYCLIC_2D , COLCTOP , CSRC_ , CTXT_ , DESCA , DESCY , DLEN_ , DTYPE_ , EI , I , IA , IACOL , IAROW , IB , ICOFFA , ICTXT , IDUM1 , IDUM2 , IHI , IHIP , IHLP , IIA , IINFO , ILCOL , ILO , ILROW , IMCOL , INDXG2P , INFO , INLQ , IOFF , IPT , IPW , IPY , IROFFA , J , JA , JJ , JJA , JY , K , L , LLD_ , LQUERY , LWMIN , LWORK , M_ , MB_ , MYCOL , MYROW , N , N_ , NB , NB_ , NPCOL , NPROW , NQ , NUMROC , ONE , ROWCTOP , RSRC_ , TAU , WORK , ZERO

Accessed arrays [ array name : associated index ]
	A	: i+1:ia+ihi-1,j+ib:ja+n-1 , ia:ia+ihi-1,j+ib:ja+ihi-1
	DESCA	: CSRC_ , CSRC_ , CSRC_ , CSRC_ , CTXT_ , MB_ , NB_ , NB_ , RSRC_
	DESCY	: CSRC_ , DLEN_
	IDUM1	: 1 , 2 , 3 , 3 , 3
	IDUM2	: 1 , 2 , 3 , 3
	NUMROC	: IHI+IROFFA, NB, MYROW, IAROW, NPROW , IHI-ILO+IOFF+1, NB, MYROW, ILROW, NPROW , JA+N-2, NB, MYCOL, DESCA( CSRC_ ), NPCOL , N-ILO+IOFF+1, NB, MYCOL, ILCOL, NPCOL
	TAU	: J , J
	WORK	: 1 , 1 , IPT , IPT , IPW , IPY , IPY , IPY

Conditional statements [ statement : associated predicate ]
	do	: `(` 10 J = JJA , MIN( JJ , NQ ) `)` , `(` 20 J = JJ , NQ `)` , `(` 30 L = 1 , IHI - ILO + IOFF - NB , NB `)`
	if	: `(` NPROW.EQ. - 1 `)` , `(` INFO.EQ.0 `)` , `(` (ILO.LT.1 .OR. ILO.GT.MAX( 1 , N ) ) `)` , `(` (IHI.LT.MIN( ILO , N ) .OR. IHI.GT.N ) `)` , `(` IROFFA.NE.ICOFFA .OR. IROFFA.NE.0 `)` , `(` (DESCA( MB_ ).NE.DESCA( NB_ ) ) `)` , `(` LWORK.LT.LWMIN .AND. .NOT.LQUERY `)` , `(` LWORK.EQ. - 1 `)` , `(` INFO.NE.0 `)` , `(` LQUERY `)` , `(` possible `)` , `(` IHI-ILO.LE.0 `)`